A little-known fact is that stainless steel actually rusts when it is not surrounded by oxygen–the opposite of most ferrous metals. In marine environments, stainless steel parts below the waterline have been found to rust. You can look this up if you wish, e.g., https://www.polymersolutions.com/blog/why-does-stainless-steel-rust/ . I have experimented with this by submerging stainless steel in water and rust definitely formed.
That being said, I don’t think it matters if the screws rust inside the epoxy-covered wood anyway. Once the glue sets they are not adding much if any structural strength. So why not just use drywall screws and cover them with the fillet material instead? In my case, I did remove them since they are no longer needed. But, in the past I have left non-stainless steel screws and brads inside epoxy-encapsulated boats for years with no ill effects. They may or may not have rusted inside the wood, but so what?